Most guests from the US will fly into Anguilla's airport (AXA) from Miami (MIA) since there is now a daily direct flight on American Airlines. A sample, but typical, flight schedule is:

To Anguilla: 10:50AM Departs MIA, 01:49PM Arrives AXA
From Anguilla: 02:40PM Departs AXA, 05:50M Arrives MIA

Another way to come Anguilla is by first flying into St. Maarten's/St. Martin's Princess Juliana Airport (SXM) which can be flown to non-stop from many US cities. Anguilla is only six miles from St. Martin, and can be reached by ferry in about 30 minutes. The public ferry arrives and departs from Marigot to Anguilla daily. Private ferries that depart across the street from the airport might be more convenient -- ferries by Fun Time Charters and Calypso Charters Anguilla. It is also possible to take a 5 minute flight from St. Maarten/St. Martin airport to Anguilla if the ferry is not your style.
It is very easy to travel to Anguilla, check with your travel agent. Anguilla is also served by a variety of smaller inter-island airlines coming to and from smaller islands close to Anguilla. These airlines include Winair, LIAT, and Carib Air.